1. STAT 104 Section 9 Daniel Moon

2. Agenda Tests of Population mean μ X Comparisons of two means F-test for equal variances Multiple Linear Regression

3. Tests of Population mean μ X Has the average price of homes increased since the 2000 census reported mean and SD figures? A survey in India showed birthweights had an average of 111 and SD of 16 ounces The national Latin Achievement test has a mean of 600 and SD of 50; Do students from Boston Latin School score above the national average on this test?

4. Agenda Tests of Population mean μ X Comparisons of two means F-test for equal variances Multiple Linear Regression

5. Comparisons of two means To determine if the length of commercials on public television increased in the past 10 years, tapes of some programs in 1996 and 2006 were analyzed Surveys were conducted to determine if adults from MA are saving more or less than those from NY Were airlines justified last month when they raised ticket prices due to an increase in passenger weight?

6. Agenda Tests of Population mean μ X Comparisons of two means F-test for equal variances Multiple Linear Regression

7. F-test for equal variances Test statistics F = larger s^2 / smaller s^2 When you calculate p-value, Don’t forget to multiply by 2 if it’s two-tail.

8. Agenda Tests of Population mean μ X Comparisons of two means F-test for equal variances Multiple Linear Regression

9. Air Pollution vs. Mortality Mean January temperature (degrees F) Annual rainfall (in inches) Median education level Percentage of non-whites in population Percentage white collar workers Average popluation per household Median income Hydrocarbons (HC) air pollution Nitrous Oxide (NOx) air pollution Sulfur Dioxide (SO2) air pollution Mortality MLR model: Y i = β 0 + β 1 X 1i + β 2 X 2i + β 3 X 3i + … + β p X pi + ε i  Residuals ε i ~ N(0, σ)  Parameters of the model: β 0, β 1, β 2, … β p, σ

10. 1 st Step: Check Normality

11. Transformation if needed

12. Step Down Approach

13. Drop Income

14. Drop LS02

15. Drop Household

16. Drop Education

17. Drop LHC

18. Conclusion This analysis shows that after adjusting for the influence of the other predictors, air pollution as measured by Nitrous Oxide is significantly associated with mortality. An increase in Nitrous Oxide is significantly associated with an increase in mortality. What others??

19. Look at the residuals